Timeline for Small quotients of smooth numbers
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 8, 2015 at 7:40 | comment | added | Kurisuto Asutora | Yes, I understand. | |
| May 4, 2015 at 17:03 | comment | added | Gerhard Paseman | @KurisutoAsutora, my intent is to support the claim that the infimum is not far from exp(-ck log k), instead of the exp (-ck) you suggest might occur. I doubt the data supports either conclusion, but the fact is that the infimum does not occur as a ratio of consecutive smooth numbers for some small k, and this is likely to make a lower bound proof harder. Even if you focus on those cases for which the infimum does occur at consecutive smooth numbers, I don't know how many there are of such cases. Gerhard "Sorry For The Machine Error" Paseman, 2015.05.04 | |
| May 1, 2015 at 10:57 | comment | added | Kurisuto Asutora | Hi Gerhard, thanks for your contribution. I have to confess that I don't know which claim is supported by your computations. Yes, in the last line you certainly get a ration which is very small. (Two 17-digit numbers differing by a 9-digit number). On the other hand, the quotient in the second displayed formula in the question is the quotient of the first 20 primes (71 is the 20-th prime), which is a 27-digit number, compared to the same number minus one, which means a difference only in the last digit. | |
| Apr 28, 2015 at 19:47 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
17 digits is too big.
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| Apr 28, 2015 at 19:26 | comment | added | Gerhard Paseman | Returning to the millions range, my program reports further improvements, one of them being 221669902,1 for $y,b$. Gerhard "Paging Experts On Stormer's Theorem" Paseman, 2015.04.28 | |
| Apr 28, 2015 at 19:11 | history | answered | Gerhard Paseman | CC BY-SA 3.0 |